{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:G3HXUT33MFKIPEG7SRX7P6KIW6","short_pith_number":"pith:G3HXUT33","schema_version":"1.0","canonical_sha256":"36cf7a4f7b61548790df946ff7f948b7b57ce1e29102bbc4fb2b6e7850cc7a3b","source":{"kind":"arxiv","id":"1102.3661","version":1},"attestation_state":"computed","paper":{"title":"Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e A. Ca\\~nizo, Mar\\'ia J. C\\'aceres, St\\'ephane Mischler","submitted_at":"2011-02-17T19:01:52Z","abstract_excerpt":"In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the operator defining the time evolution. In the present work we prove that there is also a spectral gap in weighted $L^1$ spaces, thus extending exponential convergence to a larger set of initial conditions. The main tool is an extension result in ref. [4]."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1102.3661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-17T19:01:52Z","cross_cats_sorted":[],"title_canon_sha256":"5c4bd2b11f20ef97203ddb082e2de78b5128fc190e21e5246507664ca9b971a8","abstract_canon_sha256":"9555cfde46fbf871b38411bf01176910b83bb704f6f3119031b6a23c90da31be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.327549Z","signature_b64":"Xlur/HyC5VPXDRs5oL38lX+RNq0ZEJg49AVi4SjHaawGyknccO408Hk9t4eCu4tgB8g4fE2au+zyS+HCuERoDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36cf7a4f7b61548790df946ff7f948b7b57ce1e29102bbc4fb2b6e7850cc7a3b","last_reissued_at":"2026-05-18T04:07:05.326885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.326885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jos\\'e A. Ca\\~nizo, Mar\\'ia J. C\\'aceres, St\\'ephane Mischler","submitted_at":"2011-02-17T19:01:52Z","abstract_excerpt":"In a recent result by the authors (ref. [1]) it was proved that solutions of the self-similar fragmentation equation converge to equilibrium exponentially fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the operator defining the time evolution. In the present work we prove that there is also a spectral gap in weighted $L^1$ spaces, thus extending exponential convergence to a larger set of initial conditions. The main tool is an extension result in ref. [4]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3661","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1102.3661","created_at":"2026-05-18T04:07:05.326996+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.3661v1","created_at":"2026-05-18T04:07:05.326996+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3661","created_at":"2026-05-18T04:07:05.326996+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3HXUT33MFKI","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3HXUT33MFKIPEG7","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3HXUT33","created_at":"2026-05-18T12:26:28.662955+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6","json":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6.json","graph_json":"https://pith.science/api/pith-number/G3HXUT33MFKIPEG7SRX7P6KIW6/graph.json","events_json":"https://pith.science/api/pith-number/G3HXUT33MFKIPEG7SRX7P6KIW6/events.json","paper":"https://pith.science/paper/G3HXUT33"},"agent_actions":{"view_html":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6","download_json":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6.json","view_paper":"https://pith.science/paper/G3HXUT33","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.3661&json=true","fetch_graph":"https://pith.science/api/pith-number/G3HXUT33MFKIPEG7SRX7P6KIW6/graph.json","fetch_events":"https://pith.science/api/pith-number/G3HXUT33MFKIPEG7SRX7P6KIW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6/action/storage_attestation","attest_author":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6/action/author_attestation","sign_citation":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6/action/citation_signature","submit_replication":"https://pith.science/pith/G3HXUT33MFKIPEG7SRX7P6KIW6/action/replication_record"}},"created_at":"2026-05-18T04:07:05.326996+00:00","updated_at":"2026-05-18T04:07:05.326996+00:00"}